R Notebook

Run download_data.Rmd and percentage_of_regional_richness.Rmd First!

city_data

fetch_city_data_for <- function(pool_name, include_city_name = F) {
  results_filename <- paste(paste(pool_name, 'city', 'richness', 'intercept', sep = "_"), "csv", sep = ".")
  results <- read_csv(results_filename)
  
  joined <- left_join(city_data, results)
  
  pool_size_col_name <- paste(pool_name, 'pool', 'size', sep = "_")
  
  required_columns <- c("response", pool_size_col_name, "population_growth", "rainfall_monthly_min", "rainfall_annual_average", "rainfall_monthly_max", "temperature_annual_average", "temperature_monthly_min", "temperature_monthly_max", "happiness_negative_effect", "happiness_positive_effect", "happiness_future_life", "number_of_biomes", "realm", "biome_name", "region_20km_includes_estuary", "region_50km_includes_estuary", "region_100km_includes_estuary", "city_includes_estuary", "region_20km_average_pop_density", "region_50km_average_pop_density", "region_100km_average_pop_density", "city_max_pop_density", "city_average_pop_density", "mean_population_exposure_to_pm2_5_2019", "region_20km_cultivated", "region_20km_urban", "region_50km_cultivated", "region_50km_urban", "region_100km_cultivated", "region_100km_urban", "region_20km_elevation_delta", "region_20km_mean_elevation", "region_50km_elevation_delta", "region_50km_mean_elevation", "region_100km_elevation_delta", "region_100km_mean_elevation", "city_elevation_delta", "city_mean_elevation", "urban", "shrubs", "permanent_water", "open_forest", "herbaceous_wetland", "herbaceous_vegetation", "cultivated", "closed_forest", "share_of_population_within_400m_of_open_space", "percentage_urban_area_as_streets", "percentage_urban_area_as_open_public_spaces_and_streets", "percentage_urban_area_as_open_public_spaces", "city_gdp_per_population", "city_ndvi", "city_ssm", "city_susm", "region_20km_ndvi", "region_20km_ssm", "region_20km_susm", "region_50km_ndvi", "region_50km_ssm", "region_50km_susm", "region_100km_ndvi", "region_100km_ssm", "region_100km_susm", "city_percentage_protected", "region_20km_percentage_protected", "region_50km_percentage_protected", "region_100km_percentage_protected")
  
  if (include_city_name) {
    required_columns <- append(c("name"), required_columns)
  }
  
  joined[,required_columns]
}

merlin_city_data <- fetch_city_data_for('merlin')

── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)

Joining, by = "name"

merlin_city_data

library(randomForest)
library(reshape2)
library(rpart)
library(ggplot2)
library(tidyverse)

library(multcomp)

Loading required package: mvtnorm
Loading required package: survival

Attaching package: ‘survival’

The following object is masked from ‘package:boot’:

    aml

Loading required package: TH.data
Loading required package: MASS

Attaching package: ‘MASS’

The following object is masked from ‘package:dplyr’:

    select


Attaching package: ‘TH.data’

The following object is masked from ‘package:MASS’:

    geyser

merlin_city_data_fixed <- rfImpute(response ~ ., merlin_city_data)

     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |     16.9    93.78 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    17.12    94.95 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    17.13    95.01 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    17.35    96.27 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    16.71    92.71 |

merlin_city_data_fixed

source('./random_forest_selection_functions.R')

scale_parameter_name <- function(scale, postscript) {
  paste('region', paste(scale, 'km', sep = ''), postscript, sep = '_')  
}

scale_parameters <- function(postscript) {
  c(scale_parameter_name(20, postscript), scale_parameter_name(50, postscript), scale_parameter_name(100, postscript))
}

scales_parameters_without <- function(scale_to_exclude, postscript) {
  scales <- scale_parameters(postscript)
  scales[scales != scale_parameter_name(scale_to_exclude, postscript)]
}

select_scales <- function(urban, cultivated, elevation_delta, mean_elevation, average_pop_density, includes_estuary, ssm, susm, ndv, percentage_protectedi) {
  append(
    append(
      append(
        append(
          scales_parameters_without(scale_to_exclude = urban, postscript = 'urban'),
          scales_parameters_without(scale_to_exclude = cultivated, postscript = 'cultivated')
        ),
        append(
          scales_parameters_without(scale_to_exclude = elevation_delta, postscript = 'elevation_delta'),
          scales_parameters_without(scale_to_exclude = mean_elevation, postscript = 'mean_elevation')
        )
      ),
      append(
        append(
          scales_parameters_without(scale_to_exclude = average_pop_density, postscript = 'average_pop_density'),
          scales_parameters_without(scale_to_exclude = includes_estuary, postscript = 'includes_estuary')
        ),
        append(
          scales_parameters_without(scale_to_exclude = ssm, postscript = 'ssm'),
          scales_parameters_without(scale_to_exclude = susm, postscript = 'susm')
        )
      )
    ),
    append(
      scales_parameters_without(scale_to_exclude = ndvi, postscript = 'ndvi'),
      scales_parameters_without(scale_to_exclude = percentage_protected, postscript = 'percentage_protected')
    )
  )
}

select_scales(urban = 20, cultivated = 100, elevation_delta = 20, mean_elevation = 100, average_pop_density = NA, includes_estuary = NA, ssm = 20, susm = 20, ndvi = 100, percentage_protected = NA)

 [1] "region_50km_urban"                 "region_100km_urban"                "region_20km_cultivated"            "region_50km_cultivated"            "region_50km_elevation_delta"      
 [6] "region_100km_elevation_delta"      "region_20km_mean_elevation"        "region_50km_mean_elevation"        "region_20km_average_pop_density"   "region_50km_average_pop_density"  
[11] "region_100km_average_pop_density"  "region_20km_includes_estuary"      "region_50km_includes_estuary"      "region_100km_includes_estuary"     "region_50km_ssm"                  
[16] "region_100km_ssm"                  "region_50km_susm"                  "region_100km_susm"                 "region_20km_ndvi"                  "region_50km_ndvi"                 
[21] "region_20km_percentage_protected"  "region_50km_percentage_protected"  "region_100km_percentage_protected"

select_scales(urban = , cultivated = , elevation_delta = , mean_elevation = , average_pop_density = , includes_estuary = , ssm = , susm = , ndvi =, percentage_protected = )

select_variables_from_random_forest(merlin_city_data_fixed)

 [1] "merlin_pool_size"                                        "biome_name"                                              "realm"                                                  
 [4] "region_100km_ssm"                                        "region_50km_ssm"                                         "temperature_annual_average"                             
 [7] "region_50km_elevation_delta"                             "temperature_monthly_min"                                 "region_20km_elevation_delta"                            
[10] "region_20km_urban"                                       "region_50km_susm"                                        "region_50km_urban"                                      
[13] "rainfall_monthly_min"                                    "permanent_water"                                         "region_100km_elevation_delta"                           
[16] "region_100km_cultivated"                                 "shrubs"                                                  "region_20km_cultivated"                                 
[19] "city_gdp_per_population"                                 "share_of_population_within_400m_of_open_space"           "region_20km_ndvi"                                       
[22] "happiness_positive_effect"                               "herbaceous_wetland"                                      "region_50km_average_pop_density"                        
[25] "region_50km_cultivated"                                  "city_percentage_protected"                               "region_20km_average_pop_density"                        
[28] "region_100km_urban"                                      "city_ndvi"                                               "temperature_monthly_max"                                
[31] "happiness_future_life"                                   "region_100km_average_pop_density"                        "rainfall_monthly_max"                                   
[34] "city_average_pop_density"                                "city_max_pop_density"                                    "mean_population_exposure_to_pm2_5_2019"                 
[37] "region_20km_susm"                                        "region_20km_ssm"                                         "city_susm"                                              
[40] "region_50km_percentage_protected"                        "region_100km_susm"                                       "region_100km_percentage_protected"                      
[43] "region_50km_ndvi"                                        "city_elevation_delta"                                    "city_mean_elevation"                                    
[46] "region_20km_percentage_protected"                        "rainfall_annual_average"                                 "percentage_urban_area_as_open_public_spaces_and_streets"
[49] "herbaceous_vegetation"                                   "urban"                                                   "region_100km_ndvi"                                      
[52] "cultivated"                                              "region_20km_mean_elevation"                              "city_ssm"                                               
[55] "region_100km_mean_elevation"                             "region_50km_mean_elevation"                              "population_growth"                                      
[58] "percentage_urban_area_as_streets"                        "happiness_negative_effect"                               "percentage_urban_area_as_open_public_spaces"            
[61] "closed_forest"                                           "open_forest"                                            

select_variables_from_random_forest(merlin_city_data_fixed_single_scale)

 [1] "merlin_pool_size"                                        "biome_name"                                              "realm"                                                  
 [4] "region_100km_ssm"                                        "temperature_annual_average"                              "temperature_monthly_min"                                
 [7] "region_50km_elevation_delta"                             "rainfall_monthly_min"                                    "permanent_water"                                        
[10] "region_50km_susm"                                        "region_20km_ndvi"                                        "region_20km_urban"                                      
[13] "shrubs"                                                  "city_gdp_per_population"                                 "happiness_positive_effect"                              
[16] "city_percentage_protected"                               "region_100km_cultivated"                                 "share_of_population_within_400m_of_open_space"          
[19] "rainfall_monthly_max"                                    "city_ndvi"                                               "temperature_monthly_max"                                
[22] "city_average_pop_density"                                "region_50km_average_pop_density"                         "rainfall_annual_average"                                
[25] "city_mean_elevation"                                     "region_50km_percentage_protected"                        "percentage_urban_area_as_open_public_spaces_and_streets"
[28] "urban"                                                   "cultivated"                                              "percentage_urban_area_as_open_public_spaces"            
[31] "happiness_negative_effect"                               "region_20km_mean_elevation"                              "city_susm"                                              
[34] "city_ssm"                                                "percentage_urban_area_as_streets"                        "closed_forest"                                          
[37] "open_forest"                                            

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size")])

[1] "Mean  18.3291184364462 , SD:  0.239909691174696 , Mean + SD:  18.5690281276209"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name")])

[1] "Mean  15.8873631581584 , SD:  0.180232366982089 , Mean + SD:  16.0675955251404"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm")])

[1] "Mean  14.085087335964 , SD:  0.181457368755455 , Mean + SD:  14.2665447047195"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm")])

[1] "Mean  14.7500741158013 , SD:  0.199005244777679 , Mean + SD:  14.949079360579"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average")])

[1] "Mean  15.0736086564802 , SD:  0.233605527261414 , Mean + SD:  15.3072141837417"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min")])

[1] "Mean  15.2264915835863 , SD:  0.193099894838028 , Mean + SD:  15.4195914784244"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta")])

[1] "Mean  15.2378145280404 , SD:  0.248172547588966 , Mean + SD:  15.4859870756294"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min")])

[1] "Mean  14.9140396251349 , SD:  0.197619251055124 , Mean + SD:  15.11165887619"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water")])

[1] "Mean  14.8536445422209 , SD:  0.254378052303436 , Mean + SD:  15.1080225945243"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm")])

[1] "Mean  15.5273572141801 , SD:  0.273890093511612 , Mean + SD:  15.8012473076917"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm", "region_20km_ndvi")])

[1] "Mean  15.3186439115578 , SD:  0.227215081868521 , Mean + SD:  15.5458589934263"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm", "region_20km_ndvi", "region_20km_urban")])

[1] "Mean  15.1681755140829 , SD:  0.224510713543485 , Mean + SD:  15.3926862276264"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm", "region_20km_ndvi", "region_20km_urban", "shrubs")])

[1] "Mean  15.1902125119541 , SD:  0.226152938160966 , Mean + SD:  15.4163654501151"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm", "region_20km_ndvi", "region_20km_urban", "shrubs",  "city_gdp_per_population")])

[1] "Mean  15.2065363289081 , SD:  0.255119486173744 , Mean + SD:  15.4616558150818"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm", "region_20km_ndvi", "region_20km_urban", "shrubs",  "city_gdp_per_population", "happiness_positive_effect")])

[1] "Mean  15.2791920489499 , SD:  0.262306992952203 , Mean + SD:  15.5414990419021"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm", "region_20km_ndvi", "region_20km_urban", "shrubs",  "city_gdp_per_population", "happiness_positive_effect", "city_percentage_protected")])

[1] "Mean  15.2653808786396 , SD:  0.243375155516205 , Mean + SD:  15.5087560341558"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm", "region_20km_ndvi", "region_20km_urban", "shrubs",  "city_gdp_per_population", "happiness_positive_effect", "city_percentage_protected", "region_100km_cultivated")])

[1] "Mean  15.4694621878868 , SD:  0.281353351110609 , Mean + SD:  15.7508155389974"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm", "region_20km_ndvi", "region_20km_urban", "shrubs",  "city_gdp_per_population", "happiness_positive_effect", "city_percentage_protected", "region_100km_cultivated", "share_of_population_within_400m_of_open_space")])

[1] "Mean  15.2754584376954 , SD:  0.245564947611728 , Mean + SD:  15.5210233853072"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm", "region_20km_ndvi", "region_20km_urban", "shrubs",  "city_gdp_per_population", "happiness_positive_effect", "city_percentage_protected", "region_100km_cultivated", "share_of_population_within_400m_of_open_space", "rainfall_monthly_max")])

[1] "Mean  15.5025730033436 , SD:  0.254677972901481 , Mean + SD:  15.7572509762451"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm", "region_20km_ndvi", "region_20km_urban", "shrubs",  "city_gdp_per_population", "happiness_positive_effect", "city_percentage_protected", "region_100km_cultivated", "share_of_population_within_400m_of_open_space", "rainfall_monthly_max", "city_ndvi")])

[1] "Mean  15.5523641989269 , SD:  0.237597135507919 , Mean + SD:  15.7899613344348"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm", "region_20km_ndvi", "region_20km_urban", "shrubs",  "city_gdp_per_population", "happiness_positive_effect", "city_percentage_protected", "region_100km_cultivated", "share_of_population_within_400m_of_open_space", "rainfall_monthly_max", "city_ndvi", "temperature_monthly_max")])

[1] "Mean  15.6384411101055 , SD:  0.220167702046869 , Mean + SD:  15.8586088121524"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm", "region_20km_ndvi", "region_20km_urban", "shrubs",  "city_gdp_per_population", "happiness_positive_effect", "city_percentage_protected", "region_100km_cultivated", "share_of_population_within_400m_of_open_space", "rainfall_monthly_max", "city_ndvi", "temperature_monthly_max", "city_average_pop_density")])

[1] "Mean  15.8461770285193 , SD:  0.290074490489128 , Mean + SD:  16.1362515190084"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm", "region_20km_ndvi", "region_20km_urban", "shrubs",  "city_gdp_per_population", "happiness_positive_effect", "city_percentage_protected", "region_100km_cultivated", "share_of_population_within_400m_of_open_space", "rainfall_monthly_max", "city_ndvi", "temperature_monthly_max", "city_average_pop_density", "region_50km_average_pop_density")])

[1] "Mean  15.8811819521739 , SD:  0.297186312599319 , Mean + SD:  16.1783682647732"

create_fifty_rows_of_oob(merlin_city_data_fixed[,c("response", "merlin_pool_size", "biome_name", "realm", "region_100km_ssm", "temperature_annual_average", "temperature_monthly_min", "region_50km_elevation_delta",  "rainfall_monthly_min", "permanent_water", "region_50km_susm", "region_20km_ndvi", "region_20km_urban", "shrubs",  "city_gdp_per_population", "happiness_positive_effect", "city_percentage_protected", "region_100km_cultivated", "share_of_population_within_400m_of_open_space", "rainfall_monthly_max", "city_ndvi", "temperature_monthly_max", "city_average_pop_density", "region_50km_average_pop_density", "rainfall_annual_average")])

[1] "Mean  15.8259267082361 , SD:  0.239634386030856 , Mean + SD:  16.0655610942669"

“merlin_pool_size”, “biome_name”, “realm”

birdlife_city_data <- fetch_city_data_for('birdlife')

── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)

Joining, by = "name"

birdlife_city_data

birdlife_city_data_fixed <- rfImpute(response ~ ., birdlife_city_data)

     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.552    87.89 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.512    87.25 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.559    88.00 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.703    90.27 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.738    90.84 |

birdlife_city_data_fixed

select_variables_from_random_forest(birdlife_city_data_fixed)

 [1] "population_growth"                                       "birdlife_pool_size"                                      "region_50km_ssm"                                        
 [4] "region_100km_ssm"                                        "city_ndvi"                                               "region_100km_cultivated"                                
 [7] "biome_name"                                              "region_50km_cultivated"                                  "temperature_monthly_min"                                
[10] "region_20km_ssm"                                         "percentage_urban_area_as_open_public_spaces"             "region_100km_susm"                                      
[13] "region_20km_susm"                                        "region_20km_average_pop_density"                         "permanent_water"                                        
[16] "rainfall_monthly_min"                                    "region_50km_susm"                                        "percentage_urban_area_as_open_public_spaces_and_streets"
[19] "rainfall_monthly_max"                                    "city_ssm"                                                "region_50km_average_pop_density"                        
[22] "region_100km_urban"                                      "region_100km_ndvi"                                       "region_50km_ndvi"                                       
[25] "temperature_annual_average"                              "percentage_urban_area_as_streets"                        "region_20km_ndvi"                                       
[28] "share_of_population_within_400m_of_open_space"           "mean_population_exposure_to_pm2_5_2019"                  "region_100km_average_pop_density"                       
[31] "region_20km_cultivated"                                  "city_average_pop_density"                                "realm"                                                  
[34] "region_20km_urban"                                       "region_20km_elevation_delta"                             "city_susm"                                              
[37] "shrubs"                                                  "region_50km_elevation_delta"                             "rainfall_annual_average"                                
[40] "happiness_future_life"                                   "region_50km_urban"                                       "region_100km_percentage_protected"                      
[43] "city_max_pop_density"                                    "region_100km_mean_elevation"                             "city_elevation_delta"                                   
[46] "region_20km_percentage_protected"                        "city_mean_elevation"                                     "region_50km_mean_elevation"                             
[49] "happiness_negative_effect"                               "happiness_positive_effect"                               "region_20km_mean_elevation"                             
[52] "closed_forest"                                           "region_100km_elevation_delta"                            "urban"                                                  
[55] "city_gdp_per_population"                                 "herbaceous_vegetation"                                   "city_percentage_protected"                              
[58] "open_forest"                                             "cultivated"                                              "temperature_monthly_max"                                

select_variables_from_random_forest(birdlife_city_data_fixed_single_scale)

 [1] "population_growth"                                       "region_50km_ssm"                                         "birdlife_pool_size"                                     
 [4] "biome_name"                                              "region_100km_cultivated"                                 "city_ndvi"                                              
 [7] "temperature_monthly_min"                                 "percentage_urban_area_as_open_public_spaces"             "rainfall_monthly_min"                                   
[10] "region_100km_susm"                                       "region_20km_average_pop_density"                         "city_ssm"                                               
[13] "permanent_water"                                         "rainfall_monthly_max"                                    "region_100km_urban"                                     
[16] "temperature_annual_average"                              "percentage_urban_area_as_open_public_spaces_and_streets" "region_20km_elevation_delta"                            
[19] "share_of_population_within_400m_of_open_space"           "shrubs"                                                  "mean_population_exposure_to_pm2_5_2019"                 
[22] "city_average_pop_density"                                "percentage_urban_area_as_streets"                        "rainfall_annual_average"                                
[25] "city_susm"                                               "region_100km_ndvi"                                       "happiness_future_life"                                  
[28] "happiness_negative_effect"                               "closed_forest"                                           "urban"                                                  
[31] "city_mean_elevation"                                     "open_forest"                                             "happiness_positive_effect"                              
[34] "temperature_monthly_max"                                 "herbaceous_vegetation"                                  

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth")])

[1] "Mean  6.35732539091931 , SD:  0.0669192246249271 , Mean + SD:  6.42424461554424"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm")])

[1] "Mean  4.84660140753839 , SD:  0.0809873063808153 , Mean + SD:  4.9275887139192"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size")])

[1] "Mean  4.59720750518497 , SD:  0.0847385212441304 , Mean + SD:  4.6819460264291"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name")])

[1] "Mean  4.79953544345078 , SD:  0.0727373010440456 , Mean + SD:  4.87227274449482"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated")])

[1] "Mean  4.89601872208129 , SD:  0.0740660057383079 , Mean + SD:  4.9700847278196"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi")])

[1] "Mean  4.83770562806036 , SD:  0.0924105715906294 , Mean + SD:  4.93011619965098"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min")])

[1] "Mean  4.8057373947522 , SD:  0.0844941778031387 , Mean + SD:  4.89023157255534"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces")])

[1] "Mean  4.83173065533811 , SD:  0.0874008189762507 , Mean + SD:  4.91913147431437"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min")])

[1] "Mean  4.79148086117739 , SD:  0.0706327485527387 , Mean + SD:  4.86211360973013"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm")])

[1] "Mean  4.91470140038153 , SD:  0.0885243062505973 , Mean + SD:  5.00322570663213"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density")])

[1] "Mean  4.90113408062541 , SD:  0.0961754282783113 , Mean + SD:  4.99730950890372"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm")])

[1] "Mean  4.9964341603519 , SD:  0.0768191114888269 , Mean + SD:  5.07325327184073"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water")])

[1] "Mean  4.97990294565762 , SD:  0.0706673679181856 , Mean + SD:  5.0505703135758"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water", "rainfall_monthly_max")])

[1] "Mean  4.99512840273475 , SD:  0.0942210618369954 , Mean + SD:  5.08934946457175"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water", "rainfall_monthly_max", "region_100km_urban")])

[1] "Mean  4.97268472007057 , SD:  0.10396874824783 , Mean + SD:  5.0766534683184"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water", "rainfall_monthly_max", "region_100km_urban", "temperature_annual_average")])

[1] "Mean  5.04114679155501 , SD:  0.0847207533308739 , Mean + SD:  5.12586754488588"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water", "rainfall_monthly_max", "region_100km_urban", "temperature_annual_average", "percentage_urban_area_as_open_public_spaces_and_streets")])

[1] "Mean  5.02111793795206 , SD:  0.092420920073587 , Mean + SD:  5.11353885802564"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water", "rainfall_monthly_max", "region_100km_urban", "temperature_annual_average", "percentage_urban_area_as_open_public_spaces_and_streets", "region_20km_elevation_delta")])

[1] "Mean  5.04087475473546 , SD:  0.0801326834604886 , Mean + SD:  5.12100743819595"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water", "rainfall_monthly_max", "region_100km_urban", "temperature_annual_average", "percentage_urban_area_as_open_public_spaces_and_streets", "region_20km_elevation_delta", "share_of_population_within_400m_of_open_space")])

[1] "Mean  5.05522409906614 , SD:  0.0925279259536348 , Mean + SD:  5.14775202501977"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water", "rainfall_monthly_max", "region_100km_urban", "temperature_annual_average", "percentage_urban_area_as_open_public_spaces_and_streets", "region_20km_elevation_delta", "share_of_population_within_400m_of_open_space", "shrubs")])

[1] "Mean  5.05563861451361 , SD:  0.093232830904438 , Mean + SD:  5.14887144541805"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water", "rainfall_monthly_max", "region_100km_urban", "temperature_annual_average", "percentage_urban_area_as_open_public_spaces_and_streets", "region_20km_elevation_delta", "share_of_population_within_400m_of_open_space", "shrubs", "mean_population_exposure_to_pm2_5_2019")])

[1] "Mean  5.05966342869761 , SD:  0.0806786305744567 , Mean + SD:  5.14034205927207"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water", "rainfall_monthly_max", "region_100km_urban", "temperature_annual_average", "percentage_urban_area_as_open_public_spaces_and_streets", "region_20km_elevation_delta", "share_of_population_within_400m_of_open_space", "shrubs", "mean_population_exposure_to_pm2_5_2019", "city_average_pop_density")])

[1] "Mean  5.12335838078195 , SD:  0.0778399806226634 , Mean + SD:  5.20119836140461"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water", "rainfall_monthly_max", "region_100km_urban", "temperature_annual_average", "percentage_urban_area_as_open_public_spaces_and_streets", "region_20km_elevation_delta", "share_of_population_within_400m_of_open_space", "shrubs", "mean_population_exposure_to_pm2_5_2019", "city_average_pop_density", "percentage_urban_area_as_streets")])

[1] "Mean  5.13879647218586 , SD:  0.0845418790784688 , Mean + SD:  5.22333835126433"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water", "rainfall_monthly_max", "region_100km_urban", "temperature_annual_average", "percentage_urban_area_as_open_public_spaces_and_streets", "region_20km_elevation_delta", "share_of_population_within_400m_of_open_space", "shrubs", "mean_population_exposure_to_pm2_5_2019", "city_average_pop_density", "percentage_urban_area_as_streets", "rainfall_annual_average")])

[1] "Mean  5.17392341305297 , SD:  0.0855140683449177 , Mean + SD:  5.25943748139789"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water", "rainfall_monthly_max", "region_100km_urban", "temperature_annual_average", "percentage_urban_area_as_open_public_spaces_and_streets", "region_20km_elevation_delta", "share_of_population_within_400m_of_open_space", "shrubs", "mean_population_exposure_to_pm2_5_2019", "city_average_pop_density", "percentage_urban_area_as_streets", "rainfall_annual_average", "city_susm")])

[1] "Mean  5.24351131619425 , SD:  0.0804843612125177 , Mean + SD:  5.32399567740677"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water", "rainfall_monthly_max", "region_100km_urban", "temperature_annual_average", "percentage_urban_area_as_open_public_spaces_and_streets", "region_20km_elevation_delta", "share_of_population_within_400m_of_open_space", "shrubs", "mean_population_exposure_to_pm2_5_2019", "city_average_pop_density", "percentage_urban_area_as_streets", "rainfall_annual_average", "city_susm", "region_100km_ndvi")])

[1] "Mean  5.30537718299019 , SD:  0.0820416774624035 , Mean + SD:  5.38741886045259"

create_fifty_rows_of_oob(birdlife_city_data_fixed[,c("response", "population_growth", "region_50km_ssm", "birdlife_pool_size", "biome_name", "region_100km_cultivated", "city_ndvi", "temperature_monthly_min", "percentage_urban_area_as_open_public_spaces", "rainfall_monthly_min", "region_100km_susm", "region_20km_average_pop_density", "city_ssm", "permanent_water", "rainfall_monthly_max", "region_100km_urban", "temperature_annual_average", "percentage_urban_area_as_open_public_spaces_and_streets", "region_20km_elevation_delta", "share_of_population_within_400m_of_open_space", "shrubs", "mean_population_exposure_to_pm2_5_2019", "city_average_pop_density", "percentage_urban_area_as_streets", "rainfall_annual_average", "city_susm", "region_100km_ndvi", "happiness_future_life")])

[1] "Mean  5.28047296957072 , SD:  0.104728547457597 , Mean + SD:  5.38520151702831"

“population_growth”, “region_50km_ssm”, “birdlife_pool_size”

So….
Merlin: “merlin_pool_size”, “biome_name”, “realm” Birdlife: “population_growth”, “region_50km_ssm”, “birdlife_pool_size”
```r ggplot(merlin_city_data_fixed, aes(x = merlin_pool_size, y = response, color = realm)) + geom_point() + geom_smooth(method = “glm”, se = F) + theme(legend.position = “bottom”)
```
`geom_smooth()` using formula 'y ~ x'
```r ggplot(merlin_city_data_fixed, aes(x = merlin_pool_size, y = response, color = biome_name)) + geom_point() + geom_smooth(method = “glm”, se = F) + theme(legend.position = “bottom”)
```
`geom_smooth()` using formula 'y ~ x'
```r ggplot(birdlife_city_data_fixed, aes(x = birdlife_pool_size, y = response, color = region_50km_ssm)) + geom_point() + geom_smooth(method = “glm”, se = F) + theme(legend.position = “bottom”)
```
`geom_smooth()` using formula 'y ~ x'
```r ggplot(birdlife_city_data_fixed, aes(x = birdlife_pool_size, y = response, color = population_growth)) + geom_point() + geom_smooth(method = “glm”, se = F) + theme(legend.position = “bottom”)
```
`geom_smooth()` using formula 'y ~ x'
```r ggplot(merlin_city_data_fixed, aes(y = response, x = population_growth)) + geom_point() + geom_smooth(method = “glm”, se = F)
```
`geom_smooth()` using formula 'y ~ x'
```r ggplot(birdlife_city_data_fixed, aes(y = response, x = population_growth)) + geom_point() + geom_smooth(method = “glm”, se = F)
```
`geom_smooth()` using formula 'y ~ x'
```r ggplot(merlin_city_data_fixed, aes(y = response, x = region_50km_ssm)) + geom_point() + geom_smooth(method = “glm”, se = F)
```
`geom_smooth()` using formula 'y ~ x'
```r ggplot(birdlife_city_data_fixed, aes(y = response, x = region_50km_ssm)) + geom_point() + geom_smooth(method = “glm”, se = F)
```
`geom_smooth()` using formula 'y ~ x'

Try Modelling

library(boot)

merlin_city_data_fixed_no_boreal <- merlin_city_data_fixed[merlin_city_data_fixed$biome_name != 'Boreal Forests/Taiga',]
birdlife_city_data_fixed_no_boreal <- birdlife_city_data_fixed[birdlife_city_data_fixed$biome_name != 'Boreal Forests/Taiga',]

test_model <- function(data, formula) {
  fit <- glm(formula, data = data)
  
  cv.glm(data, fit)$delta

  print(paste("R2", with(summary(fit), 1 - deviance/null.deviance)))
  print(paste("CV Delta", cv.glm(data, fit)$delta))
  print(paste("CV Delta", cv.glm(data, fit)$delta[1] - cv.glm(data, fit)$delta[2]))
}

test_model(merlin_city_data_fixed_no_boreal, response ~ merlin_pool_size)

[1] "R2 0.285894381786357"
[1] "CV Delta 13.2924069067549" "CV Delta 13.290989425668" 
[1] "CV Delta 0.0014174810869001"

test_model(birdlife_city_data_fixed_no_boreal, response ~ birdlife_pool_size)

[1] "R2 0.132747072834318"
[1] "CV Delta 5.61376539055778" "CV Delta 5.61321468528147"
[1] "CV Delta 0.000550705276301855"

test_model(merlin_city_data_fixed_no_boreal, response ~ merlin_pool_size + realm)

[1] "R2 0.355479718662977"
[1] "CV Delta 13.1013113338907" "CV Delta 13.0956030666681"
[1] "CV Delta 0.00570826722257856"

test_model(birdlife_city_data_fixed_no_boreal, response ~ birdlife_pool_size + realm)

[1] "R2 0.215771844466201"
[1] "CV Delta 5.38032952583311" "CV Delta 5.37866865996081"
[1] "CV Delta 0.00166086587230829"

test_model(merlin_city_data_fixed_no_boreal, response ~ merlin_pool_size + biome_name)

[1] "R2 0.370210675877385"
[1] "CV Delta 13.3828176878773" "CV Delta 13.3745769694536"
[1] "CV Delta 0.00824071842369101"

test_model(birdlife_city_data_fixed_no_boreal, response ~ birdlife_pool_size + biome_name)

[1] "R2 0.223013658291514"
[1] "CV Delta 5.9146455418679"  "CV Delta 5.91040383901086"
[1] "CV Delta 0.00424170285703518"

test_model(merlin_city_data_fixed_no_boreal, response ~ merlin_pool_size + biome_name + realm)

[1] "R2 0.404911112981243"
[1] "CV Delta 14.2088898476971" "CV Delta 14.1942054055947"
[1] "CV Delta 0.0146844421024106"

test_model(birdlife_city_data_fixed_no_boreal, response ~ birdlife_pool_size + biome_name + realm)

[1] "R2 0.282011390214033"
[1] "CV Delta 5.61291700874679" "CV Delta 5.60841587721211"
[1] "CV Delta 0.00450113153467768"

test_model(merlin_city_data_fixed_no_boreal, response ~ merlin_pool_size + population_growth)

[1] "R2 0.286929092142329"
[1] "CV Delta 13.5753866440016" "CV Delta 13.5727869610531"
[1] "CV Delta 0.00259968294847468"

test_model(birdlife_city_data_fixed_no_boreal, response ~ birdlife_pool_size + population_growth)

[1] "R2 0.134196770612853"
[1] "CV Delta 5.73874002430138" "CV Delta 5.73766284305409"
[1] "CV Delta 0.00107718124729139"

test_model(merlin_city_data_fixed_no_boreal, response ~ merlin_pool_size + population_growth + region_50km_ssm)

[1] "R2 0.290846971284311"
[1] "CV Delta 13.7387732818639" "CV Delta 13.7352820567926"
[1] "CV Delta 0.00349122507122068"

test_model(birdlife_city_data_fixed_no_boreal, response ~ birdlife_pool_size + population_growth + region_50km_ssm)

[1] "R2 0.151946781581196"
[1] "CV Delta 5.6860363390934"  "CV Delta 5.68473754059936"
[1] "CV Delta 0.00129879849403824"

test_model(merlin_city_data_fixed_no_boreal, response ~ merlin_pool_size + population_growth + region_50km_ssm + biome_name + realm)

[1] "R2 0.409838701070553"
[1] "CV Delta 14.5182790115777" "CV Delta 14.5020009668314"
[1] "CV Delta 0.0162780447462367"

test_model(birdlife_city_data_fixed_no_boreal, response ~ birdlife_pool_size + population_growth + region_50km_ssm + biome_name + realm)

[1] "R2 0.287701159199758"
[1] "CV Delta 5.81750910931357" "CV Delta 5.81199090164147"
[1] "CV Delta 0.00551820767210121"

test_model(merlin_city_data_fixed_no_boreal, response ~ merlin_pool_size + region_50km_ssm + biome_name + realm)

[1] "R2 0.408007484714431"
[1] "CV Delta 14.3038421650361" "CV Delta 14.2885697715507"
[1] "CV Delta 0.0152723934853718"

test_model(birdlife_city_data_fixed_no_boreal, response ~ birdlife_pool_size + region_50km_ssm + biome_name + realm)

[1] "R2 0.287698318614449"
[1] "CV Delta 5.66636239287125" "CV Delta 5.66147724370065"
[1] "CV Delta 0.00488514917060012"

test_model(merlin_city_data_fixed_no_boreal, response ~ merlin_pool_size + region_50km_ssm + realm)

[1] "R2 0.359678173824136"
[1] "CV Delta 13.2441153115841" "CV Delta 13.2375767587302"
[1] "CV Delta 0.00653855285384175"

test_model(birdlife_city_data_fixed_no_boreal, response ~ birdlife_pool_size + region_50km_ssm + realm)

[1] "R2 0.226422719550459"
[1] "CV Delta 5.38608965982801" "CV Delta 5.38414802481297"
[1] "CV Delta 0.00194163501504718"

test_model(merlin_city_data_fixed_no_boreal, response ~ merlin_pool_size + region_50km_ssm + biome_name)

[1] "R2 0.370916016196228"
[1] "CV Delta 13.5692480406954" "CV Delta 13.5602234710036"
[1] "CV Delta 0.00902456969186893"

test_model(birdlife_city_data_fixed_no_boreal, response ~ birdlife_pool_size + region_50km_ssm + biome_name)

[1] "R2 0.229572509441164"
[1] "CV Delta 5.99492133909034" "CV Delta 5.99012318220011"
[1] "CV Delta 0.00479815689022445"

AIC(
  glm(data = merlin_city_data_fixed_no_boreal, formula = response ~ merlin_pool_size + realm),
  glm(data = merlin_city_data_fixed_no_boreal, formula = response ~ merlin_pool_size + biome_name),
  glm(data = merlin_city_data_fixed_no_boreal, formula = response ~ merlin_pool_size + biome_name + realm),
  glm(data = merlin_city_data_fixed_no_boreal, formula = response ~ merlin_pool_size + population_growth),
  glm(data = merlin_city_data_fixed_no_boreal, formula = response ~ merlin_pool_size + region_50km_ssm),
  glm(data = merlin_city_data_fixed_no_boreal, formula = response ~ merlin_pool_size + population_growth + region_50km_ssm),
  glm(data = merlin_city_data_fixed_no_boreal, formula = response ~ merlin_pool_size + population_growth + region_50km_ssm + biome_name + realm),
  glm(data = merlin_city_data_fixed_no_boreal, formula = response ~ merlin_pool_size + region_50km_ssm + biome_name + realm),
  glm(data = merlin_city_data_fixed_no_boreal, formula = response ~ merlin_pool_size + region_50km_ssm + biome_name),
  glm(data = merlin_city_data_fixed_no_boreal, formula = response ~ merlin_pool_size + region_50km_ssm + realm)
)

AIC(
  glm(data = birdlife_city_data_fixed_no_boreal, formula = response ~ birdlife_pool_size + realm),
  glm(data = birdlife_city_data_fixed_no_boreal, formula = response ~ birdlife_pool_size + biome_name),
  glm(data = birdlife_city_data_fixed_no_boreal, formula = response ~ birdlife_pool_size + biome_name + realm),
  glm(data = birdlife_city_data_fixed_no_boreal, formula = response ~ birdlife_pool_size + population_growth),
  glm(data = birdlife_city_data_fixed_no_boreal, formula = response ~ birdlife_pool_size + region_50km_ssm),
  glm(data = birdlife_city_data_fixed_no_boreal, formula = response ~ birdlife_pool_size + population_growth + region_50km_ssm),
  glm(data = birdlife_city_data_fixed_no_boreal, formula = response ~ birdlife_pool_size + population_growth + region_50km_ssm + biome_name + realm)
)

merlin.fit <- glm(data = merlin_city_data_fixed, formula = response ~ merlin_pool_size + population_growth + region_50km_ssm + biome_name + realm)
plot(merlin.fit)

Warning: not plotting observations with leverage one:
  113

birdlife.fit <- glm(data = birdlife_city_data_fixed, formula = response ~ birdlife_pool_size + population_growth + region_50km_ssm + biome_name + realm)
plot(birdlife.fit)

Warning: not plotting observations with leverage one:
  113

But can we order cities based on how good they are for biodiversity?

merlin_city_data_named <- fetch_city_data_for('merlin', T)

── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)

Joining, by = "name"

birdlife_city_data_named <- fetch_city_data_for('birdlife', T)

── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)

Joining, by = "name"

merlin_city_data_fixed$residuals <- resid(merlin.fit)
birdlife_city_data_fixed$residuals <- resid(birdlife.fit)

ggplot(merlin_city_data_fixed, aes(y = response, x = residuals)) + geom_point() + geom_smooth(method = "lm", se = F)

`geom_smooth()` using formula 'y ~ x'

cor(merlin_city_data_fixed$response, merlin_city_data_fixed$residuals)

[1] 0.7665527

ggplot(birdlife_city_data_fixed, aes(y = response, x = residuals)) + geom_point() + geom_smooth(method = "lm", se = F)

`geom_smooth()` using formula 'y ~ x'

cor(birdlife_city_data_fixed$response, birdlife_city_data_fixed$residuals)

[1] 0.8398848

ordered_cities <- data.frame(
  ranked_performance = 1:nrow(merlin_city_data_named),
  merlin_base_response = merlin_city_data_named$name[order(-merlin_city_data$response)],
  birdlife_base_response = merlin_city_data_named$name[order(-birdlife_city_data$response)],
  merlin_model_residuals = merlin_city_data_named$name[order(-merlin_city_data$residuals)],
  birdlife_model_residuals = merlin_city_data_named$name[order(-birdlife_city_data$residuals)]
)
ordered_cities

write_csv(ordered_cities, "city_effect_residuals.csv")

What is going on with the response?

library(ggrepel)

merlin_city_data_fixed$name <- merlin_city_data_named$name
plot_merlin_poolsize <- ggplot(merlin_city_data_fixed, aes(y = response, x = merlin_pool_size)) + 
  geom_smooth(method = "lm", se = F) + 
  geom_point(aes(color = residuals), size = 4) + 
  geom_label_repel(aes(label = name), size = 4) +
  xlab("Pool Size") + ylab("City  Random Effect Response") +
  guides(color=guide_legend(title="Model residuals 'response ~ pool_size'")) +
  theme_bw() + theme(legend.position="bottom", legend.title=element_text(size=9), legend.text=element_text(size=8), legend.key.size = unit(1,"line")) +
  labs(title = "Merlin response given pool size")
plot_merlin_poolsize

birdlife_city_data_fixed$name <- birdlife_city_data_named$name
plot_birdlife_poolsize <- ggplot(birdlife_city_data_fixed, aes(y = response, x = birdlife_pool_size)) + 
  geom_smooth(method = "lm", se = F) + 
  geom_point(aes(color = residuals), size = 4) + 
  geom_label_repel(aes(label = name), size = 4) +
  xlab("Pool Size") + ylab("City  Random Effect Response") +
  guides(color=guide_legend(title="Model residuals 'response ~ pool_size'")) +
  theme_bw() + theme(legend.position="bottom", legend.title=element_text(size=9), legend.text=element_text(size=8), legend.key.size = unit(1,"line")) +
  labs(title = "Birdlife response given pool size")
plot_birdlife_poolsize

Summary of models

summary(merlin.fit)

Call:
glm(formula = response ~ merlin_pool_size + population_growth + 
    region_50km_ssm + biome_name + realm, data = merlin_city_data_fixed)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-7.5836  -1.9802  -0.2806   1.4883  16.1666  

Coefficients:
                                                                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                         2.558383   4.200653   0.609   0.5437    
merlin_pool_size                                                   -0.027339   0.003575  -7.647 6.55e-12 ***
population_growth                                                   0.003068   0.005114   0.600   0.5497    
region_50km_ssm                                                    -0.053173   0.072982  -0.729   0.4677    
biome_nameDeserts & Xeric Shrublands                                4.605968   3.868850   1.191   0.2363    
biome_nameFlooded Grasslands & Savannas                             0.525908   4.481070   0.117   0.9068    
biome_nameMangroves                                                 8.441618   4.591210   1.839   0.0685 .  
biome_nameMediterranean Forests, Woodlands & Scrub                  4.145677   3.732373   1.111   0.2690    
biome_nameMontane Grasslands & Shrublands                           5.023979   4.774921   1.052   0.2949    
biome_nameTemperate Broadleaf & Mixed Forests                       4.686888   3.622288   1.294   0.1983    
biome_nameTemperate Conifer Forests                                 4.317564   4.479751   0.964   0.3372    
biome_nameTemperate Grasslands, Savannas & Shrublands               5.637210   4.037582   1.396   0.1653    
biome_nameTropical & Subtropical Coniferous Forests                 7.544896   4.609955   1.637   0.1044    
biome_nameTropical & Subtropical Dry Broadleaf Forests              4.834888   3.977950   1.215   0.2267    
biome_nameTropical & Subtropical Grasslands, Savannas & Shrublands  7.209246   4.186447   1.722   0.0877 .  
biome_nameTropical & Subtropical Moist Broadleaf Forests            4.084507   3.830228   1.066   0.2885    
realmAustralasia                                                   -0.633465   2.622994  -0.242   0.8096    
realmIndomalayan                                                    1.301503   1.655451   0.786   0.4334    
realmNearctic                                                       2.083151   1.879997   1.108   0.2701    
realmNeotropic                                                      2.585444   1.767718   1.463   0.1463    
realmPalearctic                                                    -0.323305   1.843458  -0.175   0.8611    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 12.50991)

    Null deviance: 2469.6  on 136  degrees of freedom
Residual deviance: 1451.1  on 116  degrees of freedom
AIC: 756.13

Number of Fisher Scoring iterations: 2

summary(birdlife.fit)

Call:
glm(formula = response ~ birdlife_pool_size + population_growth + 
    region_50km_ssm + biome_name + realm, data = birdlife_city_data_fixed)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-5.1697  -1.2864  -0.2075   0.8359   9.4606  

Coefficients:
                                                                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                         3.639e+00  2.811e+00   1.295   0.1980    
birdlife_pool_size                                                 -1.298e-02  2.705e-03  -4.798 4.82e-06 ***
population_growth                                                  -7.172e-05  3.334e-03  -0.022   0.9829    
region_50km_ssm                                                    -4.483e-02  4.664e-02  -0.961   0.3385    
biome_nameDeserts & Xeric Shrublands                                3.037e+00  2.499e+00   1.215   0.2267    
biome_nameFlooded Grasslands & Savannas                             5.831e-01  2.904e+00   0.201   0.8412    
biome_nameMangroves                                                 3.282e+00  2.980e+00   1.101   0.2730    
biome_nameMediterranean Forests, Woodlands & Scrub                  2.506e+00  2.415e+00   1.038   0.3015    
biome_nameMontane Grasslands & Shrublands                           2.011e+00  3.094e+00   0.650   0.5170    
biome_nameTemperate Broadleaf & Mixed Forests                       3.067e+00  2.345e+00   1.308   0.1934    
biome_nameTemperate Conifer Forests                                 4.456e+00  2.907e+00   1.533   0.1280    
biome_nameTemperate Grasslands, Savannas & Shrublands               4.342e+00  2.616e+00   1.660   0.0996 .  
biome_nameTropical & Subtropical Coniferous Forests                 3.878e+00  2.988e+00   1.298   0.1969    
biome_nameTropical & Subtropical Dry Broadleaf Forests              3.043e+00  2.570e+00   1.184   0.2389    
biome_nameTropical & Subtropical Grasslands, Savannas & Shrublands  1.675e+00  2.724e+00   0.615   0.5400    
biome_nameTropical & Subtropical Moist Broadleaf Forests            1.819e+00  2.482e+00   0.733   0.4651    
realmAustralasia                                                   -1.882e+00  1.700e+00  -1.107   0.2706    
realmIndomalayan                                                   -8.270e-01  1.076e+00  -0.769   0.4436    
realmNearctic                                                      -2.992e+00  1.228e+00  -2.437   0.0163 *  
realmNeotropic                                                     -6.657e-01  1.143e+00  -0.582   0.5615    
realmPalearctic                                                    -2.961e+00  1.225e+00  -2.417   0.0172 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 5.26285)

    Null deviance: 865.45  on 136  degrees of freedom
Residual deviance: 610.49  on 116  degrees of freedom
AIC: 637.51

Number of Fisher Scoring iterations: 2

Review anovas

birdlife.biome.anovoa <- aov(response ~ biome_name, data=birdlife_city_data_fixed)
summary(birdlife.biome.anovoa)

             Df Sum Sq Mean Sq F value Pr(>F)
biome_name   12   98.7   8.225    1.33   0.21
Residuals   124  766.7   6.183               

merlin.biome.anovoa <- aov(response ~ biome_name, data=merlin_city_data_fixed)
summary(merlin.biome.anovoa)

             Df Sum Sq Mean Sq F value Pr(>F)
biome_name   12  212.3   17.69   0.972  0.479
Residuals   124 2257.3   18.20               

birdlife.realm.anovoa <- aov(response ~ realm, data=birdlife_city_data_fixed)
summary(birdlife.realm.anovoa)

             Df Sum Sq Mean Sq F value Pr(>F)
realm         5    0.0   0.000       0      1
Residuals   131  865.4   6.606               

merlin.realm.anovoa <- aov(response ~ realm, data=merlin_city_data_fixed)
summary(merlin.realm.anovoa)

             Df Sum Sq Mean Sq F value Pr(>F)
realm         5      0    0.00       0      1
Residuals   131   2470   18.85               

interaction.plot(merlin_city_data_fixed$realm, merlin_city_data_fixed$biome_name, merlin_city_data_fixed$response)

meriin.addative.anova <- aov(response ~ biome_name + realm, data=merlin_city_data_fixed) 
summary(meriin.addative.anova)

             Df Sum Sq Mean Sq F value Pr(>F)
biome_name   12  212.3  17.692   0.938  0.511
realm         5   13.9   2.785   0.148  0.980
Residuals   119 2243.4  18.852               

interaction.plot(merlin_city_data_fixed$realm, merlin_city_data_fixed$biome_name, merlin_city_data_fixed$response)

meriin.interaction.anova <- aov(response ~ biome_name * realm, data=merlin_city_data_fixed) 
summary(meriin.interaction.anova)

                  Df Sum Sq Mean Sq F value Pr(>F)
biome_name        12  212.3  17.692   0.890  0.559
realm              5   13.9   2.785   0.140  0.983
biome_name:realm  13  136.3  10.487   0.528  0.903
Residuals        106 2107.1  19.878               

Does the auto correlation go if we leave out pool size?

– Merlin

merlin_city_data_no_pool_size <- fetch_city_data_for('merlin', include_pool_size = F)
merlin_city_data_no_pool_size <- rfImpute(response ~ ., merlin_city_data_no_pool_size)
merlin_city_data_no_pool_size

select_variables_from_random_forest(merlin_city_data_no_pool_size)

exclude_merlin_2 <- !names(merlin_city_data_no_pool_size) %in% select_scales(urban = 20, cultivated = 30, elevation_delta = 50, mean_elevation = 100, average_pop_density = 50, includes_estuary = NA, ssm = 50, susm = 200, ndvi = 50, percentage_protected = 50)

merlin_city_data_no_pool_size_single_scale <- merlin_city_data_no_pool_size[,exclude_merlin_2]
select_variables_from_random_forest(merlin_city_data_no_pool_size_single_scale)

create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs", "temperature_monthly_min")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs", "temperature_monthly_min", "region_20km_urban")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_gdp_per_population")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_gdp_per_population", "city_ssm")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_gdp_per_population", "city_ssm", "city_average_pop_density")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_gdp_per_population", "city_ssm", "city_average_pop_density", "region_50km_average_pop_density")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_gdp_per_population", "city_ssm", "city_average_pop_density", "region_50km_average_pop_density", "region_50km_percentage_protected")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_gdp_per_population", "city_ssm", "city_average_pop_density", "region_50km_average_pop_density", "region_50km_percentage_protected", "temperature_monthly_max")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_gdp_per_population", "city_ssm", "city_average_pop_density", "region_50km_average_pop_density", "region_50km_percentage_protected", "temperature_monthly_max", "happiness_negative_effect")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_gdp_per_population", "city_ssm", "city_average_pop_density", "region_50km_average_pop_density", "region_50km_percentage_protected", "temperature_monthly_max", "happiness_negative_effect", "cultivated")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_gdp_per_population", "city_ssm", "city_average_pop_density", "region_50km_average_pop_density", "region_50km_percentage_protected", "temperature_monthly_max", "happiness_negative_effect", "cultivated", "mean_population_exposure_to_pm2_5_2019")])
create_fifty_rows_of_oob(merlin_city_data_no_pool_size[,c("response", "region_50km_ssm", "region_50km_elevation_delta", "permanent_water", "biome_name", "city_ndvi", "temperature_annual_average", "shrubs", "temperature_monthly_min", "region_20km_urban", "herbaceous_wetland", "city_max_pop_density", "city_gdp_per_population", "city_ssm", "city_average_pop_density", "region_50km_average_pop_density", "region_50km_percentage_protected", "temperature_monthly_max", "happiness_negative_effect", "cultivated", "mean_population_exposure_to_pm2_5_2019", "realm")])

“region_50km_ssm”, “region_50km_elevation_delta”, “permanent_water”, “biome_name”, “city_ndvi”

merlin.fit3 <- glm(data = merlin_city_data_no_pool_size, formula = response ~ region_50km_ssm + region_50km_elevation_delta + permanent_water + biome_name + city_ndvi)
plot(merlin.fit3)

Warning: not plotting observations with leverage one:
  113

with(summary(merlin.fit3), 1 - deviance/null.deviance)

[1] 0.1479997

merlin_city_data_no_pool_size$residuals <- resid(merlin.fit3)
ggplot(merlin_city_data_no_pool_size, aes(x = residuals, y = response)) + geom_point() + geom_smooth(method = "lm", se=F)

`geom_smooth()` using formula 'y ~ x'

cor(merlin_city_data_no_pool_size$response, merlin_city_data_no_pool_size$residuals)